Associated Topics || Dr. Math Home || Search Dr. Math

### One Billion Seconds

```
Date: 09/27/98 at 20:54:08
From: Galaxy Girl
Subject: Word problem

I'm trying to figure out how to solve this problem.

If I was born on 01/02/84, on what day, month, and year will I have
been alive for a billion seconds?

I already figured out that it would be 31.7 years but I don't
understand how to get it down to the exact date.
```

```
Date: 09/28/98 at 12:58:31
From: Doctor Rick
Subject: Re: Word problem

Hi. You've taken the right first step, dividing by the number of
seconds in a year, which is 60*60*24*365 = 31,536,000 seconds.

I want *you* to do your problem, so I will find when *I* turned
1 billion seconds old. I was born on Sept. 9, 1952. You can work out

We need to figure out approximately when is 31.7 years after 9/9/52,
so we can find how many leap years there are in that time period. Add
31.7 to 1952.67 (that's approximately Sept. 9, 2/3 of the way through
the year), and you get 1984.37, which is roughly May 1984. With a leap
year every 4 years, there were 8 leap years (1956, 60, 64, 68, 72, 76,
80, 84). I count 1984 because Feb. 29 is before May, but not 1952
because Feb. 29 is before September.

Now we can figure exactly how many days there were up to Sept. 9, 1983
(my birthday before the special day). It was 365*31 + 7 (an extra day
for each leap year). That makes 11,322 days. (That 8th leap day will
be used later.)

Let's go back now and figure how many days in a billion seconds. It is
1,000,000,000 / (60*60*24) = 11574.074 days. So on Sept. 9, 1983, I
had used up 11,322 days and there were 11574.074 - 11322 = 252.074
days left.

Now we just need to add up the days in each month. We think the
special day was in May. Let's see ... the days in September through
March are:

Sep  Oct  Nov  Dec  Jan  Feb  Mar  Apr
30 + 31 + 30 + 31 + 31 + 29 + 31 + 30 = 243 days

Notice that I counted a leap day in Feb. Now we're up to April 9
(remember we started on Sept. 9) We have 252 - 243 = 9 days left. That
puts the special day on April 18, 1984.

If I were going to do a lot of these calculations, I would find a
faster way. Some calendars tell you the day of the year, for instance,
Feb. 2 is the 33rd day of the year. If I found what day Sept. 9 was,
then added the number of days left and looked up what day that was, it
would make the last part go faster. But it's good to do it the way I
did at least once.

Now you do it with your birthdate. Your problem starts a few months
before mine ended. (And if you're 12, then your own birthday is a year
or two after that. I hope you'll figure it out your own billion-second
day, too.)

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Word Problems

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search